Bayesian t tests for accepting and rejecting the null hypothesis

Jeffrey N. Rouder; Paul L. Speckman; Dongchu Sun; Richard D. Morey; Geoffrey Iverson

doi:10.3758/pbr.16.2.225

journal article Apr 01, 2009

Bayesian t tests for accepting and rejecting the null hypothesis

Jeffrey N. Rouder Paul L. Speckman Dongchu Sun Richard D. Morey Geoffrey Iverson

Psychonomic Bulletin & Review Vol. 16 No. 2 pp. 225-237 · Springer Science and Business Media LLC

View at Publisher Save 10.3758/pbr.16.2.225

Topics

No keywords indexed for this article. Browse by subject →

References

58

[1]

A new look at the statistical model identification

H. Akaike

IEEE Transactions on Automatic Control 1974 10.1109/tac.1974.1100705

[2]

Ashby, F. G., & Maddox, W. T. (1992). Complex decision rules in categorization: Contrasting novice and experienced performance. Journal of Experimental Psychology: Human Perception & Performance, 18, 50–71. 10.1037/0096-1523.18.1.50

[3]

Augustin, T. (2008). Stevens’ power law and the problem of meaningfulness. Acta Psychologica, 128, 176. 10.1016/j.actpsy.2007.12.005

[4]

Berger, J. O., & Berry, D. A. (1988). Analyzing data: Is objectivity possible? American Scientist, 76, 159–165.

[5]

Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.

[6]

Clarke, F. R. (1957). Constant-ratio rule for confusion matrices in speech communication. Journal of the Acoustical Society of America, 29, 715–720. 10.1121/1.1909023

[7]

The earth is round (p < .05).

Jacob Cohen

American Psychologist 1994 10.1037/0003-066x.49.12.997

[8]

Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals based on central and noncentral distributions. Educational & Psychological Measurement, 61, 532–574. 10.1177/0013164401614002

[9]

Debner, J. A., & Jacoby, L. L. (1994). Unconscious perception: Attention, awareness, and control. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 304–317. 10.1037/0278-7393.20.2.304

[10]

Imaging unconscious semantic priming

Stanislas Dehaene, Lionel Naccache, Gurvan Le Clec'H et al.

Nature 1998 10.1038/26967

[11]

Edwards, W., Lindman, H., & Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review, 70, 193–242. 10.1037/h0044139

[12]

Egan, J. P. (1975). Signal detection theory and ROC-analysis. New York: Academic Press.

[13]

Fechner, G. T. (1966). Elements of psychophysics. New York: Holt, Rinehart & Winston. (Original work published 1860)

[14]

García-Donato, G., & Sun, D. (2007). Objective priors for hypothesis testing in one-way random effects models. Canadian Journal of Statistics, 35, 303–320. 10.1002/cjs.5550350207

[15]

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Boca Raton, FL: Chapman & Hall.

[16]

Gillispie, C. C., Fox, R., & Grattan-Guinness, I. (1997). Pierre-Simon Laplace, 1749–1827: A life in exact science. Princeton, NJ: Princeton University Press. 10.1515/9780691187983

[17]

Gönen, M., Johnson, W. O., Lu, Y., & Westfall, P. H. (2005). The Bayesian two-sample t test. American Statistician, 59, 252–257. 10.1198/000313005x55233

[18]

Goodman, S. N. (1999). Toward evidence-based medical statistics: I. The p value fallacy. Annals of Internal Medicine, 130, 995–1004. 10.7326/0003-4819-130-12-199906150-00008

[19]

Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley.

[20]

Grider, R. C., & Malmberg, K. J. (2008). Discriminating between changes in bias and changes in accuracy for recognition memory of emotional stimuli. Memory & Cognition, 36, 933–946. 10.3758/mc.36.5.933

[21]

Hawking, S. (Ed.) (2002). On the shoulders of giants: The great works of physics and astronomy. Philadelphia: Running Press.

[22]

Hays, W. L. (1994). Statistics (5th ed.). Fort Worth, TX: Harcourt Brace.

[23]

Jacoby, L. L. (1991). A process dissociation framework: Separating automatic from intentional uses of memory. Journal of Memory & Language, 30, 513–541. 10.1016/0749-596x(91)90025-f

[24]

Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford: Oxford University Press, Clarendon Press.

[25]

Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795. 10.2307/2291091

[26]

Kass, R. E., & Wasserman, L. (1995). A reference Bayesian test for nested hypotheses with large samples. Journal of the American Statistical Association, 90, 928–934. 10.2307/2291327

[27]

Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16, 345–353. 10.1111/j.0956-7976.2005.01538.x

[28]

Killeen, P. R. (2006). Beyond statistical inference: A decision theory for science. Psychonomic Bulletin & Review, 13, 549–562. 10.3758/bf03193962

[29]

Kline, R. B. (2004). Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, DC: American Psychological Association. 10.1037/10693-000

[30]

Lee, M. D., & Wagenmakers, E.-J. (2005). Bayesian statistical inference in psychology: Comment on Trafimow (2003). Psychological Review, 112, 662–668. 10.1037/0033-295x.112.3.662

[31]

Lehmann, E. L. (1993). The Fisher, Neyman—Pearson theories of testing hypotheses: One theory or two? Journal of the American Statistical Association, 88, 1242–1249. 10.2307/2291263

[32]

Liang, F., Paulo, R., Molina, G., Clyde, M. A., & Berger, J. O. (2008). Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association, 103, 410–423. 10.1198/016214507000001337

[33]

Lindley, D. V. (1957). A statistical paradox. Biometrika, 44, 187–192. 10.1093/biomet/44.1-2.187

[34]

Logan, G. D. (1988). Toward an instance theory of automatization. Psychological Review, 95, 492–527. 10.1037/0033-295x.95.4.492

[35]

Logan, G. D. (1992). Shapes of reaction-time distributions and shapes of learning curves: A test of the instance theory of automaticity. Journal of Experimental Psychology: Learning, Memory, & Cognition, 18, 883–914. 10.1037/0278-7393.18.5.883

[36]

Luce, R. D. (1959). Individual choice behavior: A theoretical analysis. New York: Wiley.

[37]

Masson, M. E. J., & Loftus, G. R. (2003). Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology, 57, 203–220. 10.1037/h0087426

[38]

Meehl, P. E. (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting & Clinical Psychology, 46, 806–834. 10.1037/0022-006x.46.4.806

[39]

Myung, I.-J., & Pitt, M. A. (1997). Applying Occam’s razor in modeling cognition: A Bayesian approach. Psychonomic Bulletin & Review, 4, 79–95. 10.3758/bf03210778

[40]

Plant, E. A., & Peruche, B. M. (2005). The consequences of race for police officers’ responses to criminal suspects. Psychological Science, 16, 180–183. 10.1111/j.0956-7976.2005.00800.x

[41]

Bayesian Model Selection in Social Research

Adrian E. Raftery

Sociological Methodology 1995 10.2307/271063

[42]

Reingold, E. M., & Merikle, P. M. (1988). Using direct and indirect measures to study perception without awareness. Perception & Psychophysics, 44, 563–575. 10.3758/bf03207490

[43]

Rouder, J. N., & Lu, J. (2005). An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychonomic Bulletin & Review, 12, 573–604. 10.3758/bf03196750

[44]

Rouder, J. N., & Morey, R. D. (2005). Relational and arelational confidence intervals: A comment on Fidler, Thomason, Cumming, Finch, and Leeman (2004). Psychological Science, 16, 77–79. 10.1111/j.0956-7976.2005.00783.x

[45]

Rouder, J. N., Morey, R. D., Speckman, P. L., & Pratte, M. S. (2007). Detecting chance: A solution to the null sensitivity problem in subliminal priming. Psychonomic Bulletin & Review, 14, 597–605. 10.3758/bf03196808

[46]

Rouder, J. N., & Ratcliff, R. (2004). Comparing categorization models. Journal of Experimental Psychology: General, 133, 63–82. 10.1037/0096-3445.133.1.63

[47]

Estimating the Dimension of a Model

Gideon Schwarz

The Annals of Statistics 1978 10.1214/aos/1176344136

[48]

Sellke, T., Bayarri, M. J., & Berger, J. O. (2001). Calibration of p values for testing precise null hypotheses. American Statistician, 55, 62–71. 10.1198/000313001300339950

[49]

Shepard, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22, 325–345. 10.1007/bf02288967

[50]

Shibley Hyde, J. (2005). The gender similarities hypothesis. American Psychologist, 60, 581–592. 10.1037/0003-066x.60.6.581

Showing 50 of 58 references

Cited By

2,976

Perceiving inter-leg speed differences while walking on a split-belt treadmill

Carl Müller, Karl Kopiske · 2025

Scientific Reports

Sensorimotor adaptation impedes perturbation detection in grasping

Carl Müller, Alexandra Bendixen · 2024

Psychonomic Bulletin & Review

Electrophysiological dynamics of salience, default mode, and frontoparietal networks during episodic memory formation and recall revealed through multi-experiment iEEG replication

Anup Das, Vinod Menon · 2024

eLife

Somatosensory omissions reveal action‐related predictive processing

Tjerk T. Dercksen, Andreas Widmann · 2023

Human Brain Mapping

A cross-species assessment of behavioral flexibility in compulsive disorders

Nabil Benzina, Karim N’Diaye · 2021

Communications Biology

A Bayesian approach to analysing cortico-cortical associative stimulation induced increases in the excitability of corticospinal projections in humans

Richard G. Carson, Antonio Capozio · 2020

Experimental Brain Research

The peripheral preview effect with faces: Combined EEG and eye-tracking suggests multiple stages of trans-saccadic predictive and non-predictive processing

Christoph Huber-Huber, Antimo Buonocore · 2019

NeuroImage

Decoding the status of working memory representations in preparation of visual selection

Ingmar E.J. de Vries, Joram van Driel · 2019

NeuroImage

Catecholamines alter the intrinsic variability of cortical population activity and perception

Thomas Pfeffer, Arthur-Ervin Avramiea · 2018

PLOS Biology

Targeted Right Medial Temporal Lobe tDCS and Associative Spatial and Non-Spatial Memory

Tad T. Brunyé, Erika K. Hussey · 2018

Journal of Cognitive Enhancement

A theory of working memory without consciousness or sustained activity

Darinka Trübutschek, Sébastien Marti · 2017

eLife

Active Listening Delays Attentional Disengagement and Saccadic Eye Movements

Benjamin D. Lester, Shaun P. Vecera · 2017

Psychonomic Bulletin & Review

Dissociable Decoding of Spatial Attention and Working Memory from EEG Oscillations and Sustained Potentials

Gi-Yeul Bae, Steven J. Luck · 2017

The Journal of Neuroscience

The Testing Effect Is Alive and Well with Complex Materials

Jeffrey D. Karpicke, William R. Aue · 2015

Educational Psychology Review

Common (and multiple) neural substrates for static and dynamic motion after-effects: A rTMS investigation

Gianluca Campana, Marcello Maniglia · 2013

Cortex

MorePower 6.0 for ANOVA with relational confidence intervals and Bayesian analysis

Jamie I. D. Campbell, Valerie A. Thompson · 2012

Behavior Research Methods

Metrics

2,976

Citations

58

References

Details

Published: Apr 01, 2009
Vol/Issue: 16(2)
Pages: 225-237
License: View

Authors

Cite This Article

Jeffrey N. Rouder, Paul L. Speckman, Dongchu Sun, et al. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16(2), 225-237. https://doi.org/10.3758/pbr.16.2.225

Bayesian t tests for accepting and rejecting the null hypothesis

You May Also Like